Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.961 |
Dual form | 1960.2.q.q.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.20711 | − | 2.09077i | −0.696923 | − | 1.20711i | −0.969528 | − | 0.244981i | \(-0.921218\pi\) |
0.272605 | − | 0.962126i | \(-0.412115\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.41421 | + | 2.44949i | −0.471405 | + | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41421 | + | 4.18154i | 0.727913 | + | 1.26078i | 0.957764 | + | 0.287556i | \(0.0928428\pi\) |
−0.229851 | + | 0.973226i | \(0.573824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.82843 | + | 3.16693i | 0.443459 | + | 0.768093i | 0.997943 | − | 0.0641009i | \(-0.0204179\pi\) |
−0.554485 | + | 0.832194i | \(0.687085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | − | 4.89898i | 0.648886 | − | 1.12390i | −0.334504 | − | 0.942394i | \(-0.608569\pi\) |
0.983389 | − | 0.181509i | \(-0.0580980\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.20711 | − | 7.28692i | 0.877242 | − | 1.51943i | 0.0228877 | − | 0.999738i | \(-0.492714\pi\) |
0.854355 | − | 0.519690i | \(-0.173953\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.17157 | −0.403251 | −0.201625 | − | 0.979463i | \(-0.564622\pi\) | ||||
−0.201625 | + | 0.979463i | \(0.564622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.41421 | − | 4.18154i | −0.433606 | − | 0.751027i | 0.563575 | − | 0.826065i | \(-0.309426\pi\) |
−0.997181 | + | 0.0750380i | \(0.976092\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.82843 | − | 10.0951i | 1.01460 | − | 1.75734i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82843 | − | 4.89898i | 0.464991 | − | 0.805387i | −0.534211 | − | 0.845351i | \(-0.679391\pi\) |
0.999201 | + | 0.0399642i | \(0.0127244\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.41421 | + | 4.18154i | 0.386584 | + | 0.669582i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.171573 | −0.0267952 | −0.0133976 | − | 0.999910i | \(-0.504265\pi\) | ||||
−0.0133976 | + | 0.999910i | \(0.504265\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.8995 | 1.96715 | 0.983577 | − | 0.180488i | \(-0.0577676\pi\) | ||||
0.983577 | + | 0.180488i | \(0.0577676\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | + | 2.44949i | 0.210819 | + | 0.365148i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.171573 | − | 0.297173i | 0.0250265 | − | 0.0433471i | −0.853241 | − | 0.521517i | \(-0.825366\pi\) |
0.878267 | + | 0.478170i | \(0.158700\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.41421 | − | 7.64564i | 0.618114 | − | 1.07060i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.82843 | − | 4.89898i | −0.388514 | − | 0.672927i | 0.603736 | − | 0.797185i | \(-0.293678\pi\) |
−0.992250 | + | 0.124258i | \(0.960345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.82843 | 0.651065 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.6569 | −1.80889 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | − | 3.46410i | −0.260378 | − | 0.450988i | 0.705965 | − | 0.708247i | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.32843 | + | 4.03295i | −0.298125 | + | 0.516367i | −0.975707 | − | 0.219080i | \(-0.929694\pi\) |
0.677582 | + | 0.735447i | \(0.263028\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | + | 1.73205i | −0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.44975 | − | 5.97514i | −0.421454 | − | 0.729979i | 0.574628 | − | 0.818415i | \(-0.305147\pi\) |
−0.996082 | + | 0.0884353i | \(0.971813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −20.3137 | −2.44548 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.82843 | − | 6.63103i | −0.448084 | − | 0.776103i | 0.550178 | − | 0.835048i | \(-0.314560\pi\) |
−0.998261 | + | 0.0589442i | \(0.981227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.20711 | + | 2.09077i | −0.139385 | + | 0.241421i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.74264 | + | 8.21449i | 0.526960 | + | 0.912722i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.2426 | 1.45357 | 0.726784 | − | 0.686866i | \(-0.241014\pi\) | ||||
0.726784 | + | 0.686866i | \(0.241014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65685 | 0.396642 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.62132 | + | 4.54026i | 0.281035 | + | 0.486767i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.32843 | + | 14.4253i | −0.882812 | + | 1.52907i | −0.0346099 | + | 0.999401i | \(0.511019\pi\) |
−0.848202 | + | 0.529673i | \(0.822314\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.82843 | + | 10.0951i | −0.604380 | + | 1.04682i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82843 | − | 4.89898i | −0.290191 | − | 0.502625i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.6569 | −1.37257 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.74264 | + | 4.75039i | 0.272903 | + | 0.472682i | 0.969604 | − | 0.244680i | \(-0.0786829\pi\) |
−0.696701 | + | 0.717362i | \(0.745350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.20711 | − | 9.01897i | 0.513071 | − | 0.888666i | −0.486814 | − | 0.873506i | \(-0.661841\pi\) |
0.999885 | − | 0.0151600i | \(-0.00482576\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.20711 | − | 7.28692i | 0.406716 | − | 0.704453i | −0.587803 | − | 0.809004i | \(-0.700007\pi\) |
0.994520 | + | 0.104551i | \(0.0333404\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.15685 | + | 3.73578i | 0.206589 | + | 0.357823i | 0.950638 | − | 0.310302i | \(-0.100430\pi\) |
−0.744049 | + | 0.668125i | \(0.767097\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.6569 | −1.29625 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3137 | −1.06430 | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.20711 | − | 7.28692i | −0.392315 | − | 0.679509i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.82843 | − | 4.89898i | 0.261488 | − | 0.452911i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.15685 | + | 10.6640i | −0.559714 | + | 0.969453i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.207107 | + | 0.358719i | 0.0186742 | + | 0.0323446i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6569 | −1.38932 | −0.694661 | − | 0.719338i | \(-0.744445\pi\) | ||||
−0.694661 | + | 0.719338i | \(0.744445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.5711 | − | 26.9699i | −1.37096 | − | 2.37457i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.17157 | − | 2.02922i | 0.102361 | − | 0.177294i | −0.810296 | − | 0.586021i | \(-0.800694\pi\) |
0.912657 | + | 0.408727i | \(0.134027\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.207107 | + | 0.358719i | −0.0178249 | + | 0.0308737i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | + | 3.46410i | 0.170872 | + | 0.295958i | 0.938725 | − | 0.344668i | \(-0.112008\pi\) |
−0.767853 | + | 0.640626i | \(0.778675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4853 | 1.22863 | 0.614313 | − | 0.789063i | \(-0.289433\pi\) | ||||
0.614313 | + | 0.789063i | \(0.289433\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.828427 | −0.0697661 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.82843 | − | 8.36308i | −0.403773 | − | 0.699356i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.08579 | + | 1.88064i | −0.0901697 | + | 0.156178i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.32843 | − | 5.76500i | 0.272675 | − | 0.472288i | −0.696871 | − | 0.717197i | \(-0.745425\pi\) |
0.969546 | + | 0.244909i | \(0.0787582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.41421 | + | 14.5738i | 0.684739 | + | 1.18600i | 0.973519 | + | 0.228607i | \(0.0734171\pi\) |
−0.288780 | + | 0.957396i | \(0.593250\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.3431 | −0.836194 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.82843 | −0.387829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.6569 | − | 18.4582i | −0.850510 | − | 1.47313i | −0.880749 | − | 0.473583i | \(-0.842960\pi\) |
0.0302396 | − | 0.999543i | \(-0.490373\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.82843 | + | 11.8272i | −0.541529 | + | 0.937957i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.17157 | − | 3.76127i | 0.170091 | − | 0.294606i | −0.768361 | − | 0.640017i | \(-0.778927\pi\) |
0.938451 | + | 0.345411i | \(0.112261\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.82843 | − | 10.0951i | −0.453742 | − | 0.785905i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0711 | 0.934087 | 0.467044 | − | 0.884234i | \(-0.345319\pi\) | ||||
0.467044 | + | 0.884234i | \(0.345319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | + | 13.8564i | 0.611775 | + | 1.05963i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8284 | − | 18.7554i | 0.823270 | − | 1.42595i | −0.0799642 | − | 0.996798i | \(-0.525481\pi\) |
0.903234 | − | 0.429148i | \(-0.141186\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.82843 | + | 8.36308i | −0.362927 | + | 0.628608i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.24264 | − | 9.08052i | −0.391853 | − | 0.678710i | 0.600841 | − | 0.799369i | \(-0.294833\pi\) |
−0.992694 | + | 0.120659i | \(0.961499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.82843 | 0.730541 | 0.365271 | − | 0.930901i | \(-0.380976\pi\) | ||||
0.365271 | + | 0.930901i | \(0.380976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2426 | 0.831080 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | − | 4.89898i | −0.207950 | − | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.82843 | + | 15.2913i | −0.645599 | + | 1.11821i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2426 | − | 19.4728i | 0.813489 | − | 1.40900i | −0.0969189 | − | 0.995292i | \(-0.530899\pi\) |
0.910408 | − | 0.413712i | \(-0.135768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.65685 | − | 14.9941i | −0.623134 | − | 1.07930i | −0.988899 | − | 0.148592i | \(-0.952526\pi\) |
0.365765 | − | 0.930707i | \(-0.380808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.82843 | 0.345771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6569 | 0.830516 | 0.415258 | − | 0.909704i | \(-0.363691\pi\) | ||||
0.415258 | + | 0.909704i | \(0.363691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.343146 | − | 0.594346i | −0.0243250 | − | 0.0421321i | 0.853607 | − | 0.520918i | \(-0.174410\pi\) |
−0.877932 | + | 0.478786i | \(0.841077\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.32843 | + | 14.4253i | −0.587442 | + | 1.01748i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0857864 | + | 0.148586i | −0.00599158 | + | 0.0103777i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.8995 | + | 20.6105i | 0.827072 | + | 1.43253i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.3137 | 1.88933 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.6274 | −1.28236 | −0.641182 | − | 0.767389i | \(-0.721556\pi\) | ||||
−0.641182 | + | 0.767389i | \(0.721556\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.4853 | + | 25.0892i | 0.992515 | + | 1.71909i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.44975 | − | 11.1713i | 0.439869 | − | 0.761876i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.24264 | + | 16.0087i | −0.624560 | + | 1.08177i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.65685 | − | 6.33386i | −0.245987 | − | 0.426061i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.9706 | −1.27036 | −0.635181 | − | 0.772363i | \(-0.719075\pi\) | ||||
−0.635181 | + | 0.772363i | \(0.719075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.00000 | + | 12.1244i | 0.464606 | + | 0.804722i | 0.999184 | − | 0.0403978i | \(-0.0128625\pi\) |
−0.534577 | + | 0.845120i | \(0.679529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.171573 | + | 0.297173i | −0.0112401 | + | 0.0194684i | −0.871591 | − | 0.490234i | \(-0.836911\pi\) |
0.860351 | + | 0.509703i | \(0.170245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.171573 | − | 0.297173i | −0.0111922 | − | 0.0193854i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.65685 | −0.627280 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5147 | −0.874194 | −0.437097 | − | 0.899414i | \(-0.643993\pi\) | ||||
−0.437097 | + | 0.899414i | \(0.643993\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.8284 | − | 18.7554i | 0.694644 | − | 1.20316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.65685 | + | 9.79796i | −0.359937 | + | 0.623429i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.9853 | − | 27.6873i | −1.01303 | − | 1.75461i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4558 | −1.48052 | −0.740260 | − | 0.672321i | \(-0.765298\pi\) | ||||
−0.740260 | + | 0.672321i | \(0.765298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.6274 | 2.55422 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.41421 | − | 7.64564i | −0.276429 | − | 0.478789i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.65685 | + | 6.33386i | −0.228108 | + | 0.395095i | −0.957247 | − | 0.289270i | \(-0.906587\pi\) |
0.729139 | + | 0.684365i | \(0.239921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.07107 | − | 5.31925i | 0.190094 | − | 0.329253i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.86396 | − | 8.42463i | −0.299925 | − | 0.519485i | 0.676194 | − | 0.736724i | \(-0.263628\pi\) |
−0.976118 | + | 0.217239i | \(0.930295\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.65685 | −0.347498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.2132 | 2.46101 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.32843 | + | 4.03295i | 0.141967 | + | 0.245894i | 0.928237 | − | 0.371989i | \(-0.121324\pi\) |
−0.786270 | + | 0.617882i | \(0.787991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.65685 | − | 16.7262i | 0.586612 | − | 1.01604i | −0.408060 | − | 0.912955i | \(-0.633795\pi\) |
0.994672 | − | 0.103087i | \(-0.0328720\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.41421 | − | 4.18154i | 0.145583 | − | 0.252156i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.31371 | + | 14.3998i | 0.499522 | + | 0.865198i | 1.00000 | 0.000551476i | \(-0.000175540\pi\) | |
−0.500478 | + | 0.865750i | \(0.666842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.6569 | 0.817614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3137 | 1.51009 | 0.755045 | − | 0.655673i | \(-0.227615\pi\) | ||||
0.755045 | + | 0.655673i | \(0.227615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.00000 | + | 15.5885i | 0.534994 | + | 0.926638i | 0.999164 | + | 0.0408910i | \(0.0130196\pi\) |
−0.464169 | + | 0.885747i | \(0.653647\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.82843 | + | 11.8272i | −0.404481 | + | 0.700582i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.81371 | − | 3.14144i | 0.106689 | − | 0.184790i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.24264 | + | 12.5446i | 0.424571 | + | 0.735379i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.9706 | 0.991431 | 0.495715 | − | 0.868485i | \(-0.334906\pi\) | ||||
0.495715 | + | 0.868485i | \(0.334906\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | − | 1.73205i | −0.0580259 | − | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.41421 | + | 14.5738i | −0.486607 | + | 0.842827i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.62132 | − | 11.4685i | 0.380385 | − | 0.658846i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.32843 | + | 4.03295i | 0.133325 | + | 0.230926i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.2426 | −0.755797 | −0.377899 | − | 0.925847i | \(-0.623353\pi\) | ||||
−0.377899 | + | 0.925847i | \(0.623353\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.1421 | −1.43029 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.17157 | + | 8.95743i | 0.293253 | + | 0.507929i | 0.974577 | − | 0.224053i | \(-0.0719288\pi\) |
−0.681324 | + | 0.731982i | \(0.738596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.48528 | + | 11.2328i | −0.366570 | + | 0.634917i | −0.989027 | − | 0.147737i | \(-0.952801\pi\) |
0.622457 | + | 0.782654i | \(0.286135\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0000 | − | 19.0526i | 0.617822 | − | 1.07010i | −0.372061 | − | 0.928208i | \(-0.621349\pi\) |
0.989882 | − | 0.141890i | \(-0.0453179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.24264 | − | 9.08052i | −0.293532 | − | 0.508412i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.3137 | −1.13380 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.6863 | 1.15102 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | + | 1.73205i | 0.0554700 | + | 0.0960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.20711 | − | 9.01897i | 0.287954 | − | 0.498750i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.75736 | + | 8.23999i | −0.261488 | + | 0.452911i | −0.966638 | − | 0.256148i | \(-0.917547\pi\) |
0.705149 | + | 0.709059i | \(0.250880\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00000 | + | 13.8564i | 0.438397 | + | 0.759326i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.89949 | −0.376960 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.97056 | −0.488658 | −0.244329 | − | 0.969692i | \(-0.578568\pi\) | ||||
−0.244329 | + | 0.969692i | \(0.578568\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.6569 | + | 23.6544i | 0.741739 | + | 1.28473i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6569 | − | 20.1903i | 0.631254 | − | 1.09336i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.1569 | + | 17.5922i | −0.546827 | + | 0.947132i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.6924 | + | 21.9839i | 0.681363 | + | 1.18016i | 0.974565 | + | 0.224105i | \(0.0719458\pi\) |
−0.293202 | + | 0.956051i | \(0.594721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.17157 | −0.223299 | −0.111650 | − | 0.993748i | \(-0.535613\pi\) | ||||
−0.111650 | + | 0.993748i | \(0.535613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.828427 | 0.0442182 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1716 | + | 19.3497i | 0.594603 | + | 1.02988i | 0.993603 | + | 0.112931i | \(0.0360240\pi\) |
−0.399000 | + | 0.916951i | \(0.630643\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.24264 | + | 9.08052i | −0.276696 | + | 0.479252i | −0.970562 | − | 0.240853i | \(-0.922573\pi\) |
0.693866 | + | 0.720105i | \(0.255906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.50000 | − | 11.2583i | −0.342105 | − | 0.592544i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.7279 | 1.56031 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.65685 | −0.400778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.2071 | + | 21.1433i | 0.637206 | + | 1.10367i | 0.986043 | + | 0.166490i | \(0.0532432\pi\) |
−0.348837 | + | 0.937183i | \(0.613423\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.242641 | − | 0.420266i | 0.0126314 | − | 0.0218782i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | + | 10.3923i | −0.310668 | + | 0.538093i | −0.978507 | − | 0.206213i | \(-0.933886\pi\) |
0.667839 | + | 0.744306i | \(0.267219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.20711 | + | 2.09077i | 0.0623347 | + | 0.107967i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.34315 | 0.223683 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.3137 | 1.40301 | 0.701505 | − | 0.712664i | \(-0.252512\pi\) | ||||
0.701505 | + | 0.712664i | \(0.252512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.8995 | + | 32.7349i | 0.968250 | + | 1.67706i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.44975 | − | 16.3674i | 0.482860 | − | 0.836337i | −0.516947 | − | 0.856018i | \(-0.672931\pi\) |
0.999806 | + | 0.0196803i | \(0.00626483\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.2426 | + | 31.5972i | −0.927326 | + | 1.60617i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.65685 | + | 14.9941i | 0.438920 | + | 0.760232i | 0.997606 | − | 0.0691473i | \(-0.0220278\pi\) |
−0.558687 | + | 0.829379i | \(0.688695\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.7696 | 1.55608 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | −0.285351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.00000 | − | 3.46410i | −0.100631 | − | 0.174298i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3137 | − | 17.8639i | 0.517630 | − | 0.896562i | −0.482160 | − | 0.876083i | \(-0.660148\pi\) |
0.999790 | − | 0.0204787i | \(-0.00651902\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.84315 | − | 8.38857i | 0.241855 | − | 0.418905i | −0.719388 | − | 0.694609i | \(-0.755577\pi\) |
0.961243 | + | 0.275703i | \(0.0889108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.82843 | + | 8.36308i | 0.240521 | + | 0.416595i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.48528 | 0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.3137 | 1.35389 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.57107 | + | 2.72117i | 0.0776843 | + | 0.134553i | 0.902250 | − | 0.431212i | \(-0.141914\pi\) |
−0.824566 | + | 0.565766i | \(0.808581\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.82843 | − | 8.36308i | 0.238169 | − | 0.412520i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.62132 | − | 11.4685i | 0.325028 | − | 0.562965i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.4853 | − | 30.2854i | −0.856258 | − | 1.48308i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.31371 | −0.357298 | −0.178649 | − | 0.983913i | \(-0.557173\pi\) | ||||
−0.178649 | + | 0.983913i | \(0.557173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.6569 | 1.88402 | 0.942010 | − | 0.335585i | \(-0.108934\pi\) | ||||
0.942010 | + | 0.335585i | \(0.108934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.485281 | + | 0.840532i | 0.0235952 | + | 0.0408681i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.82843 | − | 3.16693i | 0.0886917 | − | 0.153619i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.6569 | + | 20.1903i | −0.562798 | + | 0.974795i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.41421 | − | 4.18154i | −0.116289 | − | 0.201418i | 0.802006 | − | 0.597317i | \(-0.203766\pi\) |
−0.918294 | + | 0.395899i | \(0.870433\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.31371 | −0.159247 | −0.0796233 | − | 0.996825i | \(-0.525372\pi\) | ||||
−0.0796233 | + | 0.996825i | \(0.525372\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.24264 | 0.251365 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.7990 | − | 41.2211i | −1.13846 | − | 1.97187i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8284 | + | 25.6836i | −0.707722 | + | 1.22581i | 0.257978 | + | 0.966151i | \(0.416944\pi\) |
−0.965700 | + | 0.259660i | \(0.916390\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.20711 | − | 15.9472i | 0.437443 | − | 0.757673i | −0.560049 | − | 0.828460i | \(-0.689218\pi\) |
0.997491 | + | 0.0707865i | \(0.0225509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.32843 | + | 14.4253i | 0.394805 | + | 0.683823i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.0711 | −0.760135 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.48528 | 0.447638 | 0.223819 | − | 0.974631i | \(-0.428148\pi\) | ||||
0.223819 | + | 0.974631i | \(0.428148\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.414214 | − | 0.717439i | −0.0195046 | − | 0.0337829i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.3137 | − | 35.1844i | 0.954421 | − | 1.65311i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.48528 | − | 4.30463i | 0.116257 | − | 0.201362i | −0.802025 | − | 0.597291i | \(-0.796244\pi\) |
0.918281 | + | 0.395928i | \(0.129577\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.757359 | − | 1.31178i | −0.0353505 | − | 0.0612289i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.3137 | 0.992678 | 0.496339 | − | 0.868129i | \(-0.334677\pi\) | ||||
0.496339 | + | 0.868129i | \(0.334677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.89949 | −0.227699 | −0.113849 | − | 0.993498i | \(-0.536318\pi\) | ||||
−0.113849 | + | 0.993498i | \(0.536318\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.82843 | + | 10.0951i | 0.270287 | + | 0.468151i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.93503 | − | 13.7439i | 0.367189 | − | 0.635991i | −0.621936 | − | 0.783068i | \(-0.713653\pi\) |
0.989125 | + | 0.147078i | \(0.0469868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.7279 | + | 44.5621i | −1.18548 | + | 2.05331i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.1421 | + | 53.9398i | 1.43192 | + | 2.48015i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.65685 | −0.259554 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.0000 | 0.732590 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.24264 | − | 16.0087i | −0.422307 | − | 0.731457i | 0.573858 | − | 0.818955i | \(-0.305446\pi\) |
−0.996165 | + | 0.0874978i | \(0.972113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.65685 | + | 9.79796i | −0.257930 | + | 0.446748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.00000 | + | 5.19615i | −0.136223 | + | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.14214 | − | 15.8346i | −0.414270 | − | 0.717536i | 0.581082 | − | 0.813845i | \(-0.302630\pi\) |
−0.995351 | + | 0.0963090i | \(0.969296\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.4853 | −0.474161 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4853 | 0.834229 | 0.417115 | − | 0.908854i | \(-0.363041\pi\) | ||||
0.417115 | + | 0.908854i | \(0.363041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.97056 | − | 6.87722i | −0.178825 | − | 0.309734i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.82843 | + | 11.8272i | −0.306915 | + | 0.531592i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.92893 | + | 13.7333i | −0.354948 | + | 0.614788i | −0.987109 | − | 0.160049i | \(-0.948835\pi\) |
0.632161 | + | 0.774837i | \(0.282168\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.5711 | − | 25.2378i | −0.650987 | − | 1.12754i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.0711 | 0.805749 | 0.402875 | − | 0.915255i | \(-0.368011\pi\) | ||||
0.402875 | + | 0.915255i | \(0.368011\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.48528 | 0.244092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.8640 | + | 18.8169i | 0.482485 | + | 0.835689i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.25736 | + | 14.3022i | −0.366001 | + | 0.633932i | −0.988936 | − | 0.148341i | \(-0.952607\pi\) |
0.622935 | + | 0.782273i | \(0.285940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.17157 | + | 2.02922i | −0.0517262 | + | 0.0895924i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.20711 | − | 9.01897i | −0.229453 | − | 0.397423i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.65685 | 0.0728684 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −52.2843 | −2.29502 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.31371 | − | 7.47156i | −0.188987 | − | 0.327335i | 0.755926 | − | 0.654657i | \(-0.227187\pi\) |
−0.944913 | + | 0.327322i | \(0.893854\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.9706 | + | 34.5900i | −0.873252 | + | 1.51252i | −0.0146382 | + | 0.999893i | \(0.504660\pi\) |
−0.858613 | + | 0.512624i | \(0.828674\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.82843 | − | 15.2913i | 0.384572 | − | 0.666099i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.8995 | − | 41.3951i | −1.03911 | − | 1.79979i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3137 | 0.490973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.343146 | 0.0148633 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.20711 | − | 7.28692i | −0.181889 | − | 0.315041i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.6569 | + | 21.9223i | −0.546184 | + | 0.946018i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.25736 | − | 5.64191i | 0.140045 | − | 0.242565i | −0.787468 | − | 0.616355i | \(-0.788609\pi\) |
0.927513 | + | 0.373790i | \(0.121942\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.8640 | − | 20.5490i | −0.509131 | − | 0.881841i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.31371 | 0.184779 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.7279 | −1.18556 | −0.592780 | − | 0.805364i | \(-0.701970\pi\) | ||||
−0.592780 | + | 0.805364i | \(0.701970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.58579 | − | 11.4069i | −0.281075 | − | 0.486835i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.14214 | + | 10.6385i | −0.261664 | + | 0.453215i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.82843 | + | 11.8272i | −0.289851 | + | 0.502036i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.65685 | − | 4.60181i | −0.112575 | − | 0.194985i | 0.804233 | − | 0.594314i | \(-0.202576\pi\) |
−0.916808 | + | 0.399329i | \(0.869243\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.7990 | −1.09118 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 42.6274 | 1.79973 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.03553 | + | 8.72180i | 0.212222 | + | 0.367580i | 0.952410 | − | 0.304821i | \(-0.0985965\pi\) |
−0.740187 | + | 0.672401i | \(0.765263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.65685 | + | 9.79796i | −0.237986 | + | 0.412203i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.31371 | + | 7.47156i | −0.180840 | + | 0.313224i | −0.942167 | − | 0.335144i | \(-0.891215\pi\) |
0.761327 | + | 0.648368i | \(0.224548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.48528 | − | 11.2328i | −0.271401 | − | 0.470080i | 0.697820 | − | 0.716273i | \(-0.254153\pi\) |
−0.969221 | + | 0.246193i | \(0.920820\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.2843 | −2.26776 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.41421 | −0.350897 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.1421 | + | 29.6910i | 0.713636 | + | 1.23605i | 0.963483 | + | 0.267769i | \(0.0862865\pi\) |
−0.249847 | + | 0.968285i | \(0.580380\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.8995 | + | 36.1990i | −0.868553 | + | 1.50438i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.6569 | − | 23.6544i | 0.565609 | − | 0.979664i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.82843 | − | 4.89898i | −0.116941 | − | 0.202548i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.3137 | 1.87030 | 0.935148 | − | 0.354256i | \(-0.115266\pi\) | ||||
0.935148 | + | 0.354256i | \(0.115266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.3137 | −1.12544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.0711 | − | 24.3718i | −0.578806 | − | 1.00252i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.9706 | + | 32.8580i | −0.779028 | + | 1.34932i | 0.153475 | + | 0.988153i | \(0.450954\pi\) |
−0.932503 | + | 0.361163i | \(0.882380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.828427 | + | 1.43488i | −0.0339053 | + | 0.0587256i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.31371 | + | 2.27541i | 0.0536767 | + | 0.0929707i | 0.891615 | − | 0.452794i | \(-0.149573\pi\) |
−0.837939 | + | 0.545765i | \(0.816239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0000 | 1.38689 | 0.693444 | − | 0.720510i | \(-0.256092\pi\) | ||||
0.693444 | + | 0.720510i | \(0.256092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.5147 | 0.794701 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.15685 | + | 10.6640i | 0.250312 | + | 0.433553i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.37868 | − | 16.2443i | 0.380669 | − | 0.659338i | −0.610489 | − | 0.792025i | \(-0.709027\pi\) |
0.991158 | + | 0.132687i | \(0.0423604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.343146 | + | 0.594346i | −0.0138822 | + | 0.0240447i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.51472 | − | 4.35562i | −0.101569 | − | 0.175922i | 0.810763 | − | 0.585375i | \(-0.199053\pi\) |
−0.912331 | + | 0.409453i | \(0.865719\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.414214 | 0.0167027 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.3137 | −1.42168 | −0.710838 | − | 0.703356i | \(-0.751684\pi\) | ||||
−0.710838 | + | 0.703356i | \(0.751684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.72792 | − | 9.92105i | −0.230225 | − | 0.398761i | 0.727649 | − | 0.685949i | \(-0.240613\pi\) |
−0.957874 | + | 0.287188i | \(0.907279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.74264 | + | 3.01834i | −0.0699298 | + | 0.121122i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.9706 | − | 57.1067i | −1.31672 | − | 2.28062i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.6863 | 0.824816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4853 | −0.735887 | −0.367944 | − | 0.929848i | \(-0.619938\pi\) | ||||
−0.367944 | + | 0.929848i | \(0.619938\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.4853 | + | 38.9456i | 0.893710 | + | 1.54795i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.82843 | + | 13.5592i | −0.310662 | + | 0.538082i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.9706 | − | 29.3939i | 0.671345 | − | 1.16280i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.0563 | + | 41.6668i | 0.950169 | + | 1.64574i | 0.745056 | + | 0.667002i | \(0.232423\pi\) |
0.205113 | + | 0.978738i | \(0.434244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.1421 | −1.22622 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.6213 | − | 25.3249i | −0.574823 | − | 0.995623i | −0.996061 | − | 0.0886729i | \(-0.971737\pi\) |
0.421237 | − | 0.906950i | \(-0.361596\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.65685 | − | 16.7262i | 0.379065 | − | 0.656559i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.17157 | − | 3.76127i | 0.0849802 | − | 0.147190i | −0.820403 | − | 0.571786i | \(-0.806251\pi\) |
0.905383 | + | 0.424596i | \(0.139584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.17157 | − | 2.02922i | −0.0457771 | − | 0.0792883i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.6569 | 0.844914 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.3137 | 1.37563 | 0.687813 | − | 0.725888i | \(-0.258571\pi\) | ||||
0.687813 | + | 0.725888i | \(0.258571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.8431 | − | 23.9770i | −0.538436 | − | 0.932598i | −0.998989 | − | 0.0449660i | \(-0.985682\pi\) |
0.460553 | − | 0.887632i | \(-0.347651\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.82843 | + | 15.2913i | −0.342868 | + | 0.593864i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.13604 | + | 15.8241i | −0.353749 | + | 0.612711i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.8995 | + | 39.6631i | 0.885346 | + | 1.53346i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.4853 | −0.868035 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.65685 | 0.218056 | 0.109028 | − | 0.994039i | \(-0.465226\pi\) | ||||
0.109028 | + | 0.994039i | \(0.465226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.207107 | + | 0.358719i | 0.00797154 | + | 0.0138071i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.48528 | + | 9.50079i | −0.210816 | + | 0.365145i | −0.951970 | − | 0.306190i | \(-0.900946\pi\) |
0.741154 | + | 0.671335i | \(0.234279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.8995 | − | 29.2708i | 0.647590 | − | 1.12166i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.03553 | + | 13.9180i | 0.307471 | + | 0.532556i | 0.977808 | − | 0.209501i | \(-0.0671839\pi\) |
−0.670337 | + | 0.742057i | \(0.733851\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | 0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.7990 | 1.28951 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.65685 | + | 9.79796i | 0.215509 | + | 0.373273i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3848 | − | 26.6472i | 0.585264 | − | 1.01371i | −0.409578 | − | 0.912275i | \(-0.634324\pi\) |
0.994842 | − | 0.101433i | \(-0.0323426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.24264 | − | 12.5446i | 0.274729 | − | 0.475845i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.313708 | − | 0.543359i | −0.0118826 | − | 0.0205812i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.828427 | 0.0313340 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0000 | −0.415464 | −0.207732 | − | 0.978186i | \(-0.566608\pi\) | ||||
−0.207732 | + | 0.978186i | \(0.566608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0000 | − | 27.7128i | −0.603451 | − | 1.04521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.414214 | + | 0.717439i | −0.0156002 | + | 0.0270203i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.7132 | + | 42.8045i | −0.928124 | + | 1.60756i | −0.141665 | + | 0.989915i | \(0.545246\pi\) |
−0.786459 | + | 0.617643i | \(0.788088\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.65685 | + | 9.79796i | 0.212149 | + | 0.367452i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.6274 | −1.52151 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.65685 | −0.361146 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.3137 | + | 28.2562i | 0.609247 | + | 1.05525i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.89949 | − | 11.9503i | 0.257308 | − | 0.445670i | −0.708212 | − | 0.706000i | \(-0.750498\pi\) |
0.965520 | + | 0.260330i | \(0.0838313\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.0711 | + | 20.9077i | −0.448928 | + | 0.777566i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.08579 | + | 1.88064i | 0.0403251 | + | 0.0698451i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9289 | −0.887475 | −0.443737 | − | 0.896157i | \(-0.646348\pi\) | ||||
−0.443737 | + | 0.896157i | \(0.646348\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.5858 | + | 40.8518i | 0.872352 | + | 1.51096i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.82843 | + | 3.16693i | −0.0675345 | + | 0.116973i | −0.897815 | − | 0.440372i | \(-0.854847\pi\) |
0.830281 | + | 0.557345i | \(0.188180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.6569 | − | 28.8505i | 0.613563 | − | 1.06272i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.58579 | − | 9.67487i | −0.205476 | − | 0.355896i | 0.744808 | − | 0.667279i | \(-0.232541\pi\) |
−0.950284 | + | 0.311383i | \(0.899208\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.3137 | 1.00339 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.2426 | −0.705944 | −0.352972 | − | 0.935634i | \(-0.614829\pi\) | ||||
−0.352972 | + | 0.935634i | \(0.614829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.32843 | − | 5.76500i | −0.121944 | − | 0.211213i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.7279 | + | 32.4377i | −0.685219 | + | 1.18683i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.00000 | − | 10.3923i | 0.218943 | − | 0.379221i | −0.735542 | − | 0.677479i | \(-0.763072\pi\) |
0.954485 | + | 0.298259i | \(0.0964058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.3137 | + | 49.0408i | 1.03181 | + | 1.78715i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.8284 | 0.612449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00000 | 0.218074 | 0.109037 | − | 0.994038i | \(-0.465223\pi\) | ||||
0.109037 | + | 0.994038i | \(0.465223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −49.0416 | − | 84.9426i | −1.78010 | − | 3.08322i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.9706 | − | 20.7336i | 0.433933 | − | 0.751593i | −0.563275 | − | 0.826269i | \(-0.690459\pi\) |
0.997208 | + | 0.0746761i | \(0.0237923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.17157 | + | 8.95743i | −0.186979 | + | 0.323856i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | + | 6.92820i | 0.144432 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.2548 | 1.70405 | 0.852026 | − | 0.523499i | \(-0.175374\pi\) | ||||
0.852026 | + | 0.523499i | \(0.175374\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6569 | 0.635896 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.8284 | + | 30.8797i | 0.641244 | + | 1.11067i | 0.985155 | + | 0.171665i | \(0.0549147\pi\) |
−0.343911 | + | 0.939002i | \(0.611752\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.41421 | + | 4.18154i | −0.0867211 | + | 0.150205i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.485281 | + | 0.840532i | −0.0173870 | + | 0.0301152i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.9706 | − | 50.1785i | −1.03665 | − | 1.79553i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.899495 | 0.0321453 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3137 | −0.760719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.20711 | − | 3.82282i | −0.0786749 | − | 0.136269i | 0.824004 | − | 0.566585i | \(-0.191736\pi\) |
−0.902678 | + | 0.430316i | \(0.858402\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.7426 | + | 20.3389i | −0.418049 | + | 0.724082i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.65685 | − | 8.06591i | 0.165370 | − | 0.286429i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.82843 | + | 11.8272i | 0.242179 | + | 0.419467i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6863 | 0.449372 | 0.224686 | − | 0.974431i | \(-0.427864\pi\) | ||||
0.224686 | + | 0.974431i | \(0.427864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.25483 | 0.0443928 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.5563 | − | 40.8008i | −0.832323 | − | 1.44163i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.4853 | − | 32.0174i | 0.652331 | − | 1.12987i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.62132 | − | 9.73641i | 0.197880 | − | 0.342738i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.01472 | + | 1.75754i | 0.0356756 | + | 0.0617920i | 0.883312 | − | 0.468786i | \(-0.155308\pi\) |
−0.847636 | + | 0.530578i | \(0.821975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.8579 | −0.837763 | −0.418881 | − | 0.908041i | \(-0.637578\pi\) | ||||
−0.418881 | + | 0.908041i | \(0.637578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −46.6274 | −1.63529 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.17157 | − | 3.76127i | −0.0760669 | − | 0.131752i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.4853 | − | 63.1944i | 1.27646 | − | 2.21089i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.31371 | + | 10.9357i | −0.220350 | + | 0.381657i | −0.954914 | − | 0.296882i | \(-0.904053\pi\) |
0.734564 | + | 0.678539i | \(0.237387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.0061 | + | 45.0439i | 0.906516 | + | 1.57013i | 0.818870 | + | 0.573979i | \(0.194601\pi\) |
0.0876457 | + | 0.996152i | \(0.472066\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.6569 | −0.405840 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.5269 | −1.79177 | −0.895883 | − | 0.444290i | \(-0.853456\pi\) | ||||
−0.895883 | + | 0.444290i | \(0.853456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.65685 | − | 14.9941i | −0.300665 | − | 0.520767i | 0.675622 | − | 0.737248i | \(-0.263875\pi\) |
−0.976287 | + | 0.216481i | \(0.930542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.0711 | − | 34.7641i | 0.696258 | − | 1.20595i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.03553 | − | 10.4539i | 0.208868 | − | 0.361770i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | + | 1.73205i | 0.0345651 | + | 0.0598684i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.14214 | 0.281098 | 0.140549 | − | 0.990074i | \(-0.455113\pi\) | ||||
0.140549 | + | 0.990074i | \(0.455113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2843 | −0.837389 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.5563 | − | 52.9251i | −1.05242 | − | 1.82284i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.50000 | + | 7.79423i | −0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.7279 | − | 37.6339i | 0.745700 | − | 1.29159i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.7990 | − | 41.2211i | −0.815819 | − | 1.41304i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.3137 | −1.20912 | −0.604559 | − | 0.796560i | \(-0.706651\pi\) | ||||
−0.604559 | + | 0.796560i | \(0.706651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.0000 | 0.547188 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.48528 | + | 12.9649i | 0.255692 | + | 0.442872i | 0.965083 | − | 0.261943i | \(-0.0843633\pi\) |
−0.709391 | + | 0.704815i | \(0.751030\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.31371 | − | 12.6677i | 0.249541 | − | 0.432217i | −0.713858 | − | 0.700291i | \(-0.753054\pi\) |
0.963398 | + | 0.268074i | \(0.0863871\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.0061 | + | 22.5272i | −0.442733 | + | 0.766835i | −0.997891 | − | 0.0649091i | \(-0.979324\pi\) |
0.555159 | + | 0.831745i | \(0.312658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.8284 | − | 18.7554i | −0.368178 | − | 0.637702i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.75736 | −0.297416 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.3137 | 0.655173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.89949 | + | 11.9503i | 0.233780 | + | 0.404920i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.48528 | − | 14.6969i | 0.287183 | − | 0.497416i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.1421 | + | 24.4949i | −0.477546 | + | 0.827134i | −0.999669 | − | 0.0257364i | \(-0.991807\pi\) |
0.522123 | + | 0.852870i | \(0.325140\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.4853 | − | 35.4815i | −0.690951 | − | 1.19676i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4558 | −0.823938 | −0.411969 | − | 0.911198i | \(-0.635159\pi\) | ||||
−0.411969 | + | 0.911198i | \(0.635159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.3137 | 0.986485 | 0.493242 | − | 0.869892i | \(-0.335812\pi\) | ||||
0.493242 | + | 0.869892i | \(0.335812\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.82843 | + | 8.36308i | 0.162306 | + | 0.281122i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.2071 | − | 17.6792i | 0.342721 | − | 0.593610i | −0.642216 | − | 0.766524i | \(-0.721985\pi\) |
0.984937 | + | 0.172913i | \(0.0553181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.8995 | + | 39.6631i | −0.767162 | + | 1.32876i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.970563 | − | 1.68106i | −0.0324786 | − | 0.0562547i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.4853 | −0.350484 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.6274 | 1.35651 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.24264 | + | 9.08052i | 0.174852 | + | 0.302852i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3431 | − | 17.9149i | 0.344580 | − | 0.596830i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.91421 | − | 8.51167i | 0.163354 | − | 0.282937i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.89340 | − | 3.27946i | −0.0628693 | − | 0.108893i | 0.832878 | − | 0.553457i | \(-0.186692\pi\) |
−0.895747 | + | 0.444565i | \(0.853358\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.5147 | −0.514591 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.51472 | −0.0501849 | −0.0250924 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250924 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.9706 | + | 55.3746i | 1.05807 | + | 1.83263i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.62132 | − | 9.73641i | 0.185835 | − | 0.321876i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.6274 | + | 49.5841i | −0.944331 | + | 1.63563i | −0.187247 | + | 0.982313i | \(0.559956\pi\) |
−0.757084 | + | 0.653317i | \(0.773377\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.9853 | + | 27.6873i | 0.526733 | + | 0.912328i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.65685 | −0.185996 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.7279 | + | 25.5095i | 0.483728 | + | 0.837842i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.3995 | − | 42.2612i | 0.800521 | − | 1.38654i | −0.118752 | − | 0.992924i | \(-0.537889\pi\) |
0.919273 | − | 0.393620i | \(-0.128777\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.4853 | − | 21.6251i | 0.408750 | − | 0.707975i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.82843 | + | 15.2913i | 0.288720 | + | 0.500078i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6274 | 0.869880 | 0.434940 | − | 0.900459i | \(-0.356770\pi\) | ||||
0.434940 | + | 0.900459i | \(0.356770\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.3137 | 1.02188 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.00000 | − | 8.66025i | −0.162995 | − | 0.282316i | 0.772946 | − | 0.634472i | \(-0.218782\pi\) |
−0.935942 | + | 0.352155i | \(0.885449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.721825 | + | 1.25024i | −0.0235059 | + | 0.0407134i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.4497 | + | 26.7597i | −0.502049 | + | 0.869575i | 0.497948 | + | 0.867207i | \(0.334087\pi\) |
−0.999997 | + | 0.00236799i | \(0.999246\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.65685 | + | 13.2621i | 0.248552 | + | 0.430505i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53.1127 | −1.72230 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.37258 | −0.303608 | −0.151804 | − | 0.988411i | \(-0.548508\pi\) | ||||
−0.151804 | + | 0.988411i | \(0.548508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.2426 | − | 19.4728i | −0.363803 | − | 0.630126i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.6569 | + | 21.9223i | −0.409138 | + | 0.708648i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.84315 | − | 6.65652i | 0.123972 | − | 0.214727i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.8995 | + | 20.6105i | 0.383456 | + | 0.664165i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.3137 | −0.557348 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.2426 | −1.06901 | −0.534506 | − | 0.845165i | \(-0.679502\pi\) | ||||
−0.534506 | + | 0.845165i | \(0.679502\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.9706 | − | 43.2503i | −0.802170 | − | 1.38940i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | − | 6.92820i | 0.128366 | − | 0.222337i | −0.794678 | − | 0.607032i | \(-0.792360\pi\) |
0.923044 | + | 0.384695i | \(0.125693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.41421 | − | 4.18154i | 0.0773167 | − | 0.133916i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.1421 | + | 22.7628i | 0.420454 | + | 0.728248i | 0.995984 | − | 0.0895329i | \(-0.0285374\pi\) |
−0.575530 | + | 0.817781i | \(0.695204\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −80.4264 | −2.57044 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.2010 | −0.389548 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.30761 | − | 3.99690i | −0.0736014 | − | 0.127481i | 0.826876 | − | 0.562385i | \(-0.190116\pi\) |
−0.900477 | + | 0.434903i | \(0.856783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.82843 | − | 10.0951i | 0.185709 | − | 0.321658i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54.2696 | − | 93.9976i | 1.72567 | − | 2.98895i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.414214 | + | 0.717439i | 0.0131579 | + | 0.0227902i | 0.872529 | − | 0.488562i | \(-0.162478\pi\) |
−0.859371 | + | 0.511352i | \(0.829145\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.9706 | 0.728949 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.686292 | −0.0217569 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.8284 | − | 22.2195i | −0.406280 | − | 0.703698i | 0.588189 | − | 0.808723i | \(-0.299841\pi\) |
−0.994470 | + | 0.105025i | \(0.966508\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.17157 | + | 2.02922i | −0.0370669 | + | 0.0642018i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1960.2.q.q.961.1 | 4 | ||
7.2 | even | 3 | 1960.2.a.t.1.2 | 2 | |||
7.3 | odd | 6 | 280.2.q.d.81.2 | ✓ | 4 | ||
7.4 | even | 3 | inner | 1960.2.q.q.361.1 | 4 | ||
7.5 | odd | 6 | 1960.2.a.p.1.1 | 2 | |||
7.6 | odd | 2 | 280.2.q.d.121.2 | yes | 4 | ||
21.17 | even | 6 | 2520.2.bi.k.361.1 | 4 | |||
21.20 | even | 2 | 2520.2.bi.k.1801.1 | 4 | |||
28.3 | even | 6 | 560.2.q.j.81.1 | 4 | |||
28.19 | even | 6 | 3920.2.a.bz.1.2 | 2 | |||
28.23 | odd | 6 | 3920.2.a.bp.1.1 | 2 | |||
28.27 | even | 2 | 560.2.q.j.401.1 | 4 | |||
35.3 | even | 12 | 1400.2.bh.g.249.4 | 8 | |||
35.9 | even | 6 | 9800.2.a.br.1.1 | 2 | |||
35.13 | even | 4 | 1400.2.bh.g.849.1 | 8 | |||
35.17 | even | 12 | 1400.2.bh.g.249.1 | 8 | |||
35.19 | odd | 6 | 9800.2.a.bz.1.2 | 2 | |||
35.24 | odd | 6 | 1400.2.q.h.1201.1 | 4 | |||
35.27 | even | 4 | 1400.2.bh.g.849.4 | 8 | |||
35.34 | odd | 2 | 1400.2.q.h.401.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.d.81.2 | ✓ | 4 | 7.3 | odd | 6 | ||
280.2.q.d.121.2 | yes | 4 | 7.6 | odd | 2 | ||
560.2.q.j.81.1 | 4 | 28.3 | even | 6 | |||
560.2.q.j.401.1 | 4 | 28.27 | even | 2 | |||
1400.2.q.h.401.1 | 4 | 35.34 | odd | 2 | |||
1400.2.q.h.1201.1 | 4 | 35.24 | odd | 6 | |||
1400.2.bh.g.249.1 | 8 | 35.17 | even | 12 | |||
1400.2.bh.g.249.4 | 8 | 35.3 | even | 12 | |||
1400.2.bh.g.849.1 | 8 | 35.13 | even | 4 | |||
1400.2.bh.g.849.4 | 8 | 35.27 | even | 4 | |||
1960.2.a.p.1.1 | 2 | 7.5 | odd | 6 | |||
1960.2.a.t.1.2 | 2 | 7.2 | even | 3 | |||
1960.2.q.q.361.1 | 4 | 7.4 | even | 3 | inner | ||
1960.2.q.q.961.1 | 4 | 1.1 | even | 1 | trivial | ||
2520.2.bi.k.361.1 | 4 | 21.17 | even | 6 | |||
2520.2.bi.k.1801.1 | 4 | 21.20 | even | 2 | |||
3920.2.a.bp.1.1 | 2 | 28.23 | odd | 6 | |||
3920.2.a.bz.1.2 | 2 | 28.19 | even | 6 | |||
9800.2.a.br.1.1 | 2 | 35.9 | even | 6 | |||
9800.2.a.bz.1.2 | 2 | 35.19 | odd | 6 |